You're where i was 3 years ago, except no DC involved.
3 years ago i was shocked to find him on an adult chat site - no red flags up until that point. i wanted to leave. he promised never to do it again and gave all of the reasons your DH has given you...innocent curiosity, one thing leading to another, only 'looked' didnt 'do', only 'did' web chat didnt meet..except the once..etc. i stayed.
6 months after the initial discovery lo and behold there was a alternate social media account which pretty much all through our marriage where there were chats with several women. some of the chats included suggestion of wanting to meet. i was really angry the second time and wanted to leave. he promised to change. so i stayed
Like you, i was afraid of being alone without him.
And this little fact of how long this had gone on for i never told anyone because then i would be forced to leave and i was too scared to be on my own. So kept it secret and stayed. Only 2 people know the truth, my psychologist and my brother, everyone else i've said he cheated on me with another woman. For some reason this thing that he's done is absolutely disgusting and shames me as a person and his wife. I dont know why, but it does akin to paying hookers.
DH interchangeably says he'll never do it again and then says it is a compulsion. If its a compulsion and you dont get help how can you promise never to do it again?! For me, it was the realisation that he's not the man i thought he was so what am i still here for? I still love the man i thought he was but i dont love this man that he really is. That is when the penny dropped for me. THIS is the man that he is, the other one was/is an act.
Now, years later i realised that i just couldnt go on living with this man who i just didnt know or trust or want enough to have children with. My life pretty much stalled...maybe different for you as your kids grow but i suspect your life and your marriage will stall but you may not see it for a while as you're busy with small children.
I left. 2 months on now i couldnt be better, looking up divorce lawyers today!! It took me enough time to see the light and leave but since i first saw the light i just keep running towards it. It offers the promise of a new life that is normal, where i dont feel sick to the stomach with disgust at DH's shaming habit. I cant imagine your life with two little ones but I have met too many strong and amazing single mothers so i believe you too have the strength somewhere in you which will come out when you get to the right frame of mind to get to it.
So to answer your question, i tried to forgive and i couldnt.